Comparison of the 3D Numerical Schemes for Solving Curvature Driven Level Set Equation Based on Discrete Duality Finite Volumes
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2014)
- Volume: 53, Issue: 2, page 71-83
- ISSN: 0231-9721
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topKotorová, Dana. "Comparison of the 3D Numerical Schemes for Solving Curvature Driven Level Set Equation Based on Discrete Duality Finite Volumes." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 53.2 (2014): 71-83. <http://eudml.org/doc/262165>.
@article{Kotorová2014,
abstract = {In this work we describe two schemes for solving level set equation in 3D with a method based on finite volumes. These schemes use the so-called dual volumes as in [Coudiére, Y., Hubert, F.: A 3D discrete duality finite volume method for nonlinear elliptic equations Algoritmy 2009 (2009), 51–60.], [Hermeline, F.: A finite volume method for approximating 3D diffusion operators on general meshes Journal of Computational Physics 228, 16 (2009), 5763–5786.], where they are used for the nonlinear elliptic equations. We describe these schemes theoretically and also compare results of the numerical experiments based on exact solution using proposed schemes.},
author = {Kotorová, Dana},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Mean curvature flow; level set equation; numerical solution; semi-implicit scheme; discrete duality finite volume method (DDFV); mean curvature flow; level set equation; semi-implicit scheme; discrete duality finite volume method; numerical experiments},
language = {eng},
number = {2},
pages = {71-83},
publisher = {Palacký University Olomouc},
title = {Comparison of the 3D Numerical Schemes for Solving Curvature Driven Level Set Equation Based on Discrete Duality Finite Volumes},
url = {http://eudml.org/doc/262165},
volume = {53},
year = {2014},
}
TY - JOUR
AU - Kotorová, Dana
TI - Comparison of the 3D Numerical Schemes for Solving Curvature Driven Level Set Equation Based on Discrete Duality Finite Volumes
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2014
PB - Palacký University Olomouc
VL - 53
IS - 2
SP - 71
EP - 83
AB - In this work we describe two schemes for solving level set equation in 3D with a method based on finite volumes. These schemes use the so-called dual volumes as in [Coudiére, Y., Hubert, F.: A 3D discrete duality finite volume method for nonlinear elliptic equations Algoritmy 2009 (2009), 51–60.], [Hermeline, F.: A finite volume method for approximating 3D diffusion operators on general meshes Journal of Computational Physics 228, 16 (2009), 5763–5786.], where they are used for the nonlinear elliptic equations. We describe these schemes theoretically and also compare results of the numerical experiments based on exact solution using proposed schemes.
LA - eng
KW - Mean curvature flow; level set equation; numerical solution; semi-implicit scheme; discrete duality finite volume method (DDFV); mean curvature flow; level set equation; semi-implicit scheme; discrete duality finite volume method; numerical experiments
UR - http://eudml.org/doc/262165
ER -
References
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- Coudiére, Y., Hubert, F., A 3D discrete duality finite volume method for nonlinear elliptic equations, Algoritmy 2009 (2009), 51–60. (2009) Zbl1171.65441
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- Hermeline, F., 10.1016/j.jcp.2009.05.002, Journal of Computational Physics 228, 16 (2009), 5763–5786. (2009) Zbl1168.76340MR2542915DOI10.1016/j.jcp.2009.05.002
- Kotorová, D., Discrete duality finite volume scheme for the curvature-driven level set equation, Acta Polytechnica Hungarica 8, 3 (2011), 7–12. (2011)
- Kotorová, D., Discrete duality finite volume scheme for the curvature driven level set equation in 3D, In: Advances in architectural, civil and environmental engineering [electronic source]: 22nd Annual PhD Student Conference, Nakl. STU, Bratislava, 2012, 33–39. (2012)
- Kotorová, D., 3D numerical schemes for the level set equation based on discrete duality finite volumes, to appear.
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